If each side of a square field is increased by $12\%$, then by what percentage has the area of the field increased?

Let the initial side of the square be $s=10$.Initial Area = $s^2=10\times 10=100$.The side is increased by $12\%$:New side = $10\times \left(1+\frac{12}{100}\right)=11.2$ New Area = $(11.2{)}^2=125.44$.Percentage increase in area:
$$\text{Percentage Increase}=\frac{125.44-100}{100}\times 100=25.44\%$$
Alternative Method (Successive Percentage Formula):
$$\text{Net }\%\text{ increase}=x+y+\frac{xy}{100}$$
$$\text{Net }\%\text{ increase}=12+12+\frac{12\times 12}{100}=24+1.44=25.44\%$$